SOA Exam ASTAM Sample Question 17
Study guide: Exam ASTAM
You are given the following data from a sample of 6 claims. The ground up loss for the risk is assumed to be exponential with mean \theta.
| Loss Amount | Modification |
|---|---|
| 120 | None |
| 640 | None |
| 700 | None |
| 820 | $100 deductible |
| 1220 | $100 deductible |
| 1500 | Censored at $1500 |
Part a
Write down the likelihood function for this sample and simplify as far as possible.
Part b
Show that the Maximum Likelihood Estimate of the parameter \theta is \hat{\theta} = 960.
Part c
Estimate the standard deviation of \hat{\theta} using Cramer-Rao lower bound.
Part d
Let Y be the random variable representing the insured loss amount per claim with a limit of $1000 and no deductible. Use your fitted model to estimate E[Y].
Part e
Using the delta method, construct an approximate 80% confidence (as printed) for E[Y].
Answer this question and see the worked solution